Vertical Angles Theorem: If two angles form a pair of vertical angles, then they are congruent
Congruent Supplements Theorem- If two angles are supplements of congruent angles, then the two angles are congruent.
Reflect across two parrallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines.
Two - Column Proof: has numbered (or lettered) statements and reasons that show the logical order of an arguement.
Each statement follows from a previous.
Use any definition, postulate, theorem we already know.
If you don't have a diagram, DRAW ONE!
Given: Q is the midpoint of PR
Prove: PQ = 1/2 PR and QR = 1/2 PR
Statements Reasons 1. Q is the midpoint of PR 1. Given
2. PQ = QR 2. Definition Of Midpoint
3. PQ + QR = PR 3. Segment Addition Postulate
4. PQ + PQ = PR 4. Substitution
5. 2 = PQ = PR 5. Distributive
6.PQ = 1/2 PR 6. Division
7. QR = 1/2 PR 7. Substitution
Congruent Supplements Theorem- If two angles are supplements of congruent angles, then the two angles are congruent.
Reflect across two parrallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines.
Two - Column Proof: has numbered (or lettered) statements and reasons that show the logical order of an arguement.
Given: Q is the midpoint of PR
Prove: PQ = 1/2 PR and QR = 1/2 PR
Statements Reasons
1. Q is the midpoint of PR 1. Given
2. PQ = QR 2. Definition Of Midpoint
3. PQ + QR = PR 3. Segment Addition Postulate
4. PQ + PQ = PR 4. Substitution
5. 2 = PQ = PR 5. Distributive
6.PQ = 1/2 PR 6. Division
7. QR = 1/2 PR 7. Substitution